Test of the Universal Rise of Total Cross Sections at Super-high Energies. Muneyuki ISHIDA Meisei Univ. KEKPH07. Mar. 1-3, 2007 In collabotation with Keiji IGI. Introduction. Increase of tot. cross section σ tot is at most log 2 ν : Froissart-Martin Unitarity bound
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KEKPH07. Mar. 1-3, 2007
In collabotation with Keiji IGI
at most log2ν: Froissart-Martin Unitarity bound
it was not known whether this increase is
described by logνor log2ν in πp scattering
σtot = B log2ν＋・・・
at Super-high energies
Rise of σtot at super-high energies is universal
by COMPETE collab.,that is,
the coefficient of log2(s/s0) term is universal
for all processes with N and γ targets
(by COMPETE collab.)
Assuming universal B,σtot is fitted by log2ν for various processes:
pp, Σ-p, πp, Kp, γp
ν: energy in lab.system
B is taken to be universal from the beginning.
σπN～ σNN～・・・assumed at super-high energies!
Analysis guided strongly by theory !
σπN > σNN [Igi,Ishida’02,’05]
σπN～ 2/3 σNN [Block,Halzen’04,’05]”
is to investigate the value of
Bfor pp, pp, π±p, K±p
in order to test the universality of B
(the coeff. of log2(s/s0) terms)
with no theoretical bias.
The σtot and ρ ratio(Re f/Im f) are fitted simultaneously, using FESR as a constraint.
Imaginary part σtot
Real part ρ ratio
This gives directly a constraint for πp scattering:
For pp, Kp scatterings, problem of unphysical region. Considering N=N1 and N=N2, taking the difference.
βP’, c0, c1, c2
Fits are successful .
Bpp is somewhat smaller than Bπp, but consistent within two standard deviation. Cons.with BKp(large error).
0.2817(64) or 0.2792(59)mb byBlock,Halzen, 0.263(23), 0.249(40)sys(23)stat byIgi,Ishida’06,’05
σtot =107.1±2.6mb, ρ=0.127±0.004 in’06
ρ=0.126±0.007syst±0.004stat , in ‘05
(including Tevatron discrepancy as syst. error.)
Obtained by analyzing only crossing-even amplitudes using limited data set.